// Ceres Solver - A fast non-linear least squares minimizer
// Copyright 2015 Google Inc. All rights reserved.
// http://ceres-solver.org/
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// Author: keir@google.com (Keir Mierle)
//
// A simple example of using the Ceres minimizer.
//
// Minimize 0.5 (10 - x)^2 using analytic jacobian matrix.
#include <vector>
#include "ceres/ceres.h"
#include "glog/logging.h"

using ceres::CostFunction;
using ceres::Problem;
using ceres::SizedCostFunction;
using ceres::Solve;
using ceres::Solver;

// A CostFunction implementing analytically derivatives for the
// function f(x) = 10 - x.

//In such cases, it is possible to supply your own residual and jacobian computation code.
// To do this, define a subclass of CostFunction or SizedCostFunction
// if you know the sizes of the parameters and residuals at compile time.
class QuadraticCostFunction
        : public SizedCostFunction<1 /* number of residuals */,
                1 /* size of first parameter */> {
public:
    virtual ~QuadraticCostFunction() {}

    // 通过 Evaluate 函数自定义三个东西：参数、残差和Jacobian矩阵
    virtual bool Evaluate(
            double const *const *parameters,    // 自定义参数
            double *residuals,                  // 自定义残差
            double **jacobians                  // 自定义Jacobian矩阵
    ) const {
        double x = parameters[0][0];
        // f(x) = 10 - x.
        residuals[0] = 10 - x;
        // f'(x) = -1. Since there's only 1 parameter and that parameter
        // has 1 dimension, there is only 1 element to fill in the
        // jacobians.
        //
        // Since the Evaluate function can be called with the jacobians
        // pointer equal to NULL, the Evaluate function must check to see
        // if jacobians need to be computed.
        //
        // For this simple problem it is overkill to check if jacobians[0]
        // is NULL, but in general when writing more complex
        // CostFunctions, it is possible that Ceres may only demand the
        // derivatives w.r.t. a subset of the parameter blocks.
        if (jacobians != NULL && jacobians[0] != NULL // 自己要判断什么时候计算Jacobian
                ) {
            jacobians[0][0] = -1;
        }
        return true;
    }
};

// Minimize 0.5 (10 - x)^2 using analytic jacobian matrix.
// In some cases, using automatic differentiation is not possible.
// For example, it may be the case that it is more efficient to compute
// the derivatives in closed form instead of relying on the chain rule used by the automatic differentiation code.
int main(int argc, char **argv) {
    google::InitGoogleLogging(argv[0]);
    // The variable to solve for with its initial value. It will be
    // mutated in place by the solver.
    double x = 0.5;
    const double initial_x = x;
    // Build the problem.
    Problem problem;
    // Set up the only cost function (also known as residual).
    CostFunction *cost_function = new QuadraticCostFunction;
    problem.AddResidualBlock(cost_function, NULL, &x);
    // Run the solver!
    Solver::Options options;
    options.minimizer_progress_to_stdout = true;
    Solver::Summary summary;
    Solve(options, &problem, &summary);
    std::cout << summary.BriefReport() << "\n";
    std::cout << "x : " << initial_x << " -> " << x << "\n";
    return 0;
}